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Popular >

extreme f(x)=(6x+1)e^{8x-x^2}

Solution

extreme points

f (x) = (6 x + 1) e^{8 x - x^{2}}

Solution

Minimum (\frac{23 - 697}{12}, e^{\frac{491 - 25 697}{72}} (\frac{23 - 697}{2} + 1)), Maximum (\frac{23 + 697}{12}, e^{\frac{491 + 25 697}{72}} (\frac{23 + 697}{2} + 1))

Solution steps

f^{'} (x) = - 2 e^{- x (x - 8)} (6 x^{2} - 23 x - 7)

Find intervals:

Decreasing

: - \infty < x < \frac{23 - 697}{12},

Increasing

: \frac{23 - 697}{12} < x < \frac{23 + 697}{12},

Decreasing

: \frac{23 + 697}{12} < x < \infty

Plug

x = \frac{23 - 697}{12}

into

(6 x + 1) e^{8 x - x^{2}} : e^{\frac{491 - 25 697}{72}} (\frac{23 - 697}{2} + 1)

Minimum (\frac{23 - 697}{12}, e^{\frac{491 - 25 697}{72}} (\frac{23 - 697}{2} + 1))

Plug

x = \frac{23 + 697}{12}

into

(6 x + 1) e^{8 x - x^{2}} : e^{\frac{491 + 25 697}{72}} (\frac{23 + 697}{2} + 1)

Maximum (\frac{23 + 697}{12}, e^{\frac{491 + 25 697}{72}} (\frac{23 + 697}{2} + 1))

Minimum (\frac{23 - 697}{12}, e^{\frac{491 - 25 697}{72}} (\frac{23 - 697}{2} + 1)), Maximum (\frac{23 + 697}{12}, e^{\frac{491 + 25 697}{72}} (\frac{23 + 697}{2} + 1))

Popular Examples

extreme f(x)=x^4-3x^2,-2<= x<= 0 extreme points

f (x) = x^{4} - 3 x^{2}, - 2 \leq x \leq 0

extreme f(x)=4xe^{-x^2}extreme points

f (x) = 4 x e^{- x^{2}}

extreme y=15xe^{-0.05x}-30 extreme points

y = 15 x e^{- 0.05 x} - 30

extreme f(x)=(-4x)/(x^2+6),(0,6)extreme points

f (x) = \frac{- 4 x}{x ^{2} + 6}, (0, 6)

extreme f(x)=2x^3+15x^2-36x+7,-6<x<2 extreme points

f (x) = 2 x^{3} + 15 x^{2} - 36 x + 7, - 6 < x < 2

Frequently Asked Questions (FAQ)

What is the extreme f(x)=(6x+1)e^{8x-x^2} ?
The extreme f(x)=(6x+1)e^{8x-x^2} is